In a column still, there are numerous plates of metal, stacked like vinyl records used to be over a turntable, and these are porous due to numerous apertures. Steam drives up from the bottom and volatilises the alcohol (which boils at a lower temperature than water) which is poured in in dilute solution (the mash or wash or wine if brandy is being made) from near the top. On each plate, a mini-distillation occurs. As the vapor rises part is condensed and redistilled at greater purity (higher alcohol by volume). The more plates and therefore taller the column, the higher the proof the resultant, condensed spirit will be. Generally though a second distillation is performed in another like column (called a rectification tower) or a doubler which functions like a pot still. This increases the proof because you are starting with a high abv solution and it is simply concentrated further. It is important to understand too that in general the higher the degree of purity, the fewer the secondary constituents that remain. These are chemicals such as aldehydes, acids, higher alcohols and esters. They tend (but not always) to volatilise at a higher temperature than alcohol, so they stay behind in higher proof products with the water part of the cereal beer from which whiskey is distilled. Consider buying "Whisky" by Michael Jackson which came out last year. It has good technical explanations for the generalist on such matters and contains diagrams of such equipment.

By the way malt whisky, and cognac brandy, are simply redistilled in a succession of large pots, reboiled to gain greater purity. But they are not reboiled too often because the maker wants some of the secondary elements to stay in which give the spirits flavor, especially when converted slowly in the barrel over years by various chemical actions either amongst themselves or by interacting with wood. Vodka is essentially a high proof product (before dilution to bottling strength) which has had taken from it by multiple distillations all the secondary constituents deriving from the cereals or other materials from which the mash was made and hence is basically without flavor. Ethyl alcohol has no taste itself. Traces of the secondary elements often remain, and these do influence flavor and mouthfeel to a degree. This is even more so with the high proof whisky which is used to blend with straight whiskey and other things to make, say Kessler's, an American blended whiskey. Ditto Canadian whisky. Bourbon must by law be distilled out at under 160 proof which ensures the distillate will retain flavor via the seconday elements deriving from the fermentation of the corn and rye sugars in the mash. Under various design criteria column stills can be built and operated, sometimes variably, to produce liquors at different proofs with different flavor characteristics. I read of a still recently which can be operated and adjusted to work like a pot still or a column still. The perms and combs are endless in this area, e.g., Canadians often use an extractive distillation step designed to remove certain secondary elements (called "congeners" for convenience) which even a two-step columnar process will not remove. In some column still productions the maker literally removes at certain plate levels the secondary elements he decides should not remain in the distillate. (He knows which plate because each such element has its own volatility temperature or range. This is not done for bourbon however as far as I know). All this derives from and is a branch of chemical engineering. I have seen calculations for the design of column stills and they are very sophisticated and use advanced mathematics. But the principles can be understood by laymen. Even many commercial distillers in the past were and probably still are "practical", who acquired their expertise mainly on the job. The 'shiners of course operated by practical knowledge exclusively.